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Worksheet: Combining Functions

Q1:

Determine the common domain of the functions 𝑛 ( 𝑥 ) = 7 𝑥 7 1 and 𝑛 ( 𝑥 ) = 8 𝑥 6 4 2 2 .

  • A { 8 , 7 , 8 }
  • B { 8 , 8 }
  • C { 7 , 8 }
  • D { 8 , 7 , 8 }
  • E { 8 , 7 }

Q2:

If and are two real functions where and , determine the value of if possible.

  • A
  • B
  • C
  • Dundefined

Q3:

If and are two real functions where and , find the domain of the function .

  • A
  • B
  • C
  • D
  • E

Q4:

If where , and where , find and the domain of .

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Q5:

If where , and where , then find and its domain.

  • A ,
  • B ,
  • C ,
  • D ,

Q6:

If where , and where , find and fully simplify and the domain of .

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Q7:

If and are two real functions where and , determine the value of if possible.

  • A
  • B
  • C1
  • Dundefined

Q8:

If and are two real functions where and , determine the value of if possible.

  • A
  • B5
  • C3
  • Dundefined

Q9:

Given that , where , and , where , evaluate .

  • A
  • B724
  • C
  • D

Q10:

If where , and where , find and the domain of .

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Q11:

If 𝑓 and 𝑔 are two real functions where 𝑓 ( 𝑥 ) = 𝑥 5 𝑥 2 and 𝑔 ( 𝑥 ) = 𝑥 + 4 , determine the domain of the function ( 𝑓 𝑔 ) .

  • A [ 4 , ) { 0 , 5 }
  • B ( , 4 ]
  • C { 0 , 5 }
  • D [ 4 , )
  • E [ 4 , )

Q12:

Given that and find and state its domain.

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Q13:

Given that and find and state its domain.

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Q14:

If where , and where , find the value of if possible.

  • A16
  • B46
  • C36
  • Dundefined

Q15:

What is the domain of the quotient 𝑓 𝑔 , in terms of the domains of 𝑓 and 𝑔 ? Assume that both domains are subsets of the set of real numbers.

  • A the union of the domain of 𝑓 and the domain of 𝑔
  • B the intersection of the domain of 𝑓 and the domain of 𝑔
  • C the larger of the domain of 𝑓 and the domain of 𝑔
  • D the intersection of the domain of 𝑓 and the domain of 1 𝑔
  • Ethe difference between the domain of 𝑓 and the domain of 𝑔

Q16:

Given that and find and state its domain.

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Q17:

If and are two real functions where and , find the domain of the function .

  • A
  • B
  • C
  • D
  • E

Q18:

Given that and find and state its domain.

  • A ,
  • B ,
  • C